Breast Cancer Profile Report

Dataset statistics

Number of variables	11
Number of observations	699
Missing cells	16
Missing cells (%)	0.2%
Duplicate rows	8
Duplicate rows (%)	1.1%
Total size in memory	60.2 KiB
Average record size in memory	88.2 B

Variable types

NUM	10
CAT	1

Warnings

Dataset has 8 (1.1%) duplicate rows	Duplicates
`shape_unif` is highly correlated with `size_unif`	High correlation
`size_unif` is highly correlated with `shape_unif`	High correlation
`bare_nuclei` has 16 (2.3%) missing values	Missing

Reproduction

Analysis started	2020-12-15 03:35:48.770714
Analysis finished	2020-12-15 03:36:01.877910
Duration	13.11 seconds
Software version	pandas-profiling v2.9.0
Download configuration	config.yaml

sample
Real number (ℝ_≥0)

Distinct	645
Distinct (%)	92.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	1071704.099
Minimum	61634
Maximum	13454352
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	61634
5-th percentile	411453
Q1	870688.5
median	1171710
Q3	1238298
95-th percentile	1333890.8
Maximum	13454352
Range	13392718
Interquartile range (IQR)	367609.5

Descriptive statistics

Standard deviation	617095.7298
Coefficient of variation (CV)	0.5758079404
Kurtosis	257.7171591
Mean	1071704.099
Median Absolute Deviation (MAD)	104381
Skewness	13.67532594
Sum	749121165
Variance	3.808071398e+11
Monotocity	Not monotonic

Histogram with fixed size bins (bins=50)

Value	Count	Frequency (%)
1182404	6	0.9%
1276091	5	0.7%
1198641	3	0.4%
466906	2	0.3%
1116116	2	0.3%
1070935	2	0.3%
385103	2	0.3%
1293439	2	0.3%
1240603	2	0.3%
1277792	2	0.3%
Other values (635)	671	96.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
61634	1	0.1%
63375	1	0.1%
76389	1	0.1%
95719	1	0.1%
128059	1	0.1%

Value	Count	Frequency (%)
13454352	1	0.1%
8233704	1	0.1%
1371920	1	0.1%
1371026	1	0.1%
1369821	1	0.1%

thickness
Real number (ℝ_≥0)

Distinct	10
Distinct (%)	1.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	4.417739628
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	2
median	4
Q3	6
95-th percentile	10
Maximum	10
Range	9
Interquartile range (IQR)	4

Descriptive statistics

Standard deviation	2.815740659
Coefficient of variation (CV)	0.6373713473
Kurtosis	-0.6237154123
Mean	4.417739628
Median Absolute Deviation (MAD)	2
Skewness	0.5928585327
Sum	3088
Variance	7.928395456
Monotocity	Not monotonic

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
1	145	20.7%
5	130	18.6%
3	108	15.5%
4	80	11.4%
10	69	9.9%
2	50	7.2%
8	46	6.6%
6	34	4.9%
7	23	3.3%
9	14	2.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	145	20.7%
2	50	7.2%
3	108	15.5%
4	80	11.4%
5	130	18.6%

Value	Count	Frequency (%)
10	69	9.9%
9	14	2.0%
8	46	6.6%
7	23	3.3%
6	34	4.9%

size_unif
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	10
Distinct (%)	1.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.134477825
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	1
median	1
Q3	5
95-th percentile	10
Maximum	10
Range	9
Interquartile range (IQR)	4

Descriptive statistics

Standard deviation	3.05145911
Coefficient of variation (CV)	0.9735143395
Kurtosis	0.09880288537
Mean	3.134477825
Median Absolute Deviation (MAD)	0
Skewness	1.233136558
Sum	2191
Variance	9.3114027
Monotocity	Not monotonic

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
1	384	54.9%
10	67	9.6%
3	52	7.4%
2	45	6.4%
4	40	5.7%
5	30	4.3%
8	29	4.1%
6	27	3.9%
7	19	2.7%
9	6	0.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	384	54.9%
2	45	6.4%
3	52	7.4%
4	40	5.7%
5	30	4.3%

Value	Count	Frequency (%)
10	67	9.6%
9	6	0.9%
8	29	4.1%
7	19	2.7%
6	27	3.9%

shape_unif
Real number (ℝ_≥0)

HIGH CORRELATION

Distinct	10
Distinct (%)	1.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.207439199
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	1
median	1
Q3	5
95-th percentile	10
Maximum	10
Range	9
Interquartile range (IQR)	4

Descriptive statistics

Standard deviation	2.971912767
Coefficient of variation (CV)	0.9265686995
Kurtosis	0.007010980047
Mean	3.207439199
Median Absolute Deviation (MAD)	0
Skewness	1.161859179
Sum	2242
Variance	8.832265496
Monotocity	Not monotonic

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
1	353	50.5%
2	59	8.4%
10	58	8.3%
3	56	8.0%
4	44	6.3%
5	34	4.9%
7	30	4.3%
6	30	4.3%
8	28	4.0%
9	7	1.0%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	353	50.5%
2	59	8.4%
3	56	8.0%
4	44	6.3%
5	34	4.9%

Value	Count	Frequency (%)
10	58	8.3%
9	7	1.0%
8	28	4.0%
7	30	4.3%
6	30	4.3%

marginal_adhesion
Real number (ℝ_≥0)

Distinct	10
Distinct (%)	1.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	2.806866953
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	1
median	1
Q3	4
95-th percentile	10
Maximum	10
Range	9
Interquartile range (IQR)	3

Descriptive statistics

Standard deviation	2.855379239
Coefficient of variation (CV)	1.017283429
Kurtosis	0.9879470695
Mean	2.806866953
Median Absolute Deviation (MAD)	0
Skewness	1.524468091
Sum	1962
Variance	8.1531906
Monotocity	Not monotonic

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
1	407	58.2%
3	58	8.3%
2	58	8.3%
10	55	7.9%
4	33	4.7%
8	25	3.6%
5	23	3.3%
6	22	3.1%
7	13	1.9%
9	5	0.7%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	407	58.2%
2	58	8.3%
3	58	8.3%
4	33	4.7%
5	23	3.3%

Value	Count	Frequency (%)
10	55	7.9%
9	5	0.7%
8	25	3.6%
7	13	1.9%
6	22	3.1%

epithelial_cell_size
Real number (ℝ_≥0)

Distinct	10
Distinct (%)	1.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.21602289
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	2
median	2
Q3	4
95-th percentile	8
Maximum	10
Range	9
Interquartile range (IQR)	2

Descriptive statistics

Standard deviation	2.214299887
Coefficient of variation (CV)	0.6885211836
Kurtosis	2.169066423
Mean	3.21602289
Median Absolute Deviation (MAD)	0
Skewness	1.712171802
Sum	2248
Variance	4.903123988
Monotocity	Not monotonic

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
2	386	55.2%
3	72	10.3%
4	48	6.9%
1	47	6.7%
6	41	5.9%
5	39	5.6%
10	31	4.4%
8	21	3.0%
7	12	1.7%
9	2	0.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	47	6.7%
2	386	55.2%
3	72	10.3%
4	48	6.9%
5	39	5.6%

Value	Count	Frequency (%)
10	31	4.4%
9	2	0.3%
8	21	3.0%
7	12	1.7%
6	41	5.9%

bare_nuclei
Real number (ℝ_≥0)

MISSING

Distinct	10
Distinct (%)	1.5%
Missing	16
Missing (%)	2.3%
Infinite	0
Infinite (%)	0.0%

Mean	3.54465593
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	1
median	1
Q3	6
95-th percentile	10
Maximum	10
Range	9
Interquartile range (IQR)	5

Descriptive statistics

Standard deviation	3.64385716
Coefficient of variation (CV)	1.027986138
Kurtosis	-0.7988441354
Mean	3.54465593
Median Absolute Deviation (MAD)	0
Skewness	0.9900156547
Sum	2421
Variance	13.27769501
Monotocity	Not monotonic

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
1	402	57.5%
10	132	18.9%
5	30	4.3%
2	30	4.3%
3	28	4.0%
8	21	3.0%
4	19	2.7%
9	9	1.3%
7	8	1.1%
6	4	0.6%
(Missing)	16	2.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	402	57.5%
2	30	4.3%
3	28	4.0%
4	19	2.7%
5	30	4.3%

Value	Count	Frequency (%)
10	132	18.9%
9	9	1.3%
8	21	3.0%
7	8	1.1%
6	4	0.6%

bland_chromatin
Real number (ℝ_≥0)

Distinct	10
Distinct (%)	1.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	3.43776824
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	2
median	3
Q3	5
95-th percentile	8
Maximum	10
Range	9
Interquartile range (IQR)	3

Descriptive statistics

Standard deviation	2.438364252
Coefficient of variation (CV)	0.7092869798
Kurtosis	0.1846213115
Mean	3.43776824
Median Absolute Deviation (MAD)	1
Skewness	1.099969082
Sum	2403
Variance	5.945620227
Monotocity	Not monotonic

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
2	166	23.7%
3	165	23.6%
1	152	21.7%
7	73	10.4%
4	40	5.7%
5	34	4.9%
8	28	4.0%
10	20	2.9%
9	11	1.6%
6	10	1.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	152	21.7%
2	166	23.7%
3	165	23.6%
4	40	5.7%
5	34	4.9%

Value	Count	Frequency (%)
10	20	2.9%
9	11	1.6%
8	28	4.0%
7	73	10.4%
6	10	1.4%

normal_nucleoli
Real number (ℝ_≥0)

Distinct	10
Distinct (%)	1.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	2.86695279
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	1
median	1
Q3	4
95-th percentile	10
Maximum	10
Range	9
Interquartile range (IQR)	3

Descriptive statistics

Standard deviation	3.053633894
Coefficient of variation (CV)	1.065114816
Kurtosis	0.4742686755
Mean	2.86695279
Median Absolute Deviation (MAD)	0
Skewness	1.422261257
Sum	2004
Variance	9.324679956
Monotocity	Not monotonic

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
1	443	63.4%
10	61	8.7%
3	44	6.3%
2	36	5.2%
8	24	3.4%
6	22	3.1%
5	19	2.7%
4	18	2.6%
9	16	2.3%
7	16	2.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	443	63.4%
2	36	5.2%
3	44	6.3%
4	18	2.6%
5	19	2.7%

Value	Count	Frequency (%)
10	61	8.7%
9	16	2.3%
8	24	3.4%
7	16	2.3%
6	22	3.1%

mitoses
Real number (ℝ_≥0)

Distinct	9
Distinct (%)	1.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	1.589413448
Minimum	1
Maximum	10
Zeros	0
Zeros (%)	0.0%
Memory size	5.5 KiB

Quantile statistics

Minimum	1
5-th percentile	1
Q1	1
median	1
Q3	1
95-th percentile	5
Maximum	10
Range	9
Interquartile range (IQR)	0

Descriptive statistics

Standard deviation	1.715077943
Coefficient of variation (CV)	1.07906344
Kurtosis	12.65787807
Mean	1.589413448
Median Absolute Deviation (MAD)	0
Skewness	3.560657844
Sum	1111
Variance	2.941492349
Monotocity	Not monotonic

Histogram with fixed size bins (bins=9)

Value	Count	Frequency (%)
1	579	82.8%
2	35	5.0%
3	33	4.7%
10	14	2.0%
4	12	1.7%
7	9	1.3%
8	8	1.1%
5	6	0.9%
6	3	0.4%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	579	82.8%
2	35	5.0%
3	33	4.7%
4	12	1.7%
5	6	0.9%

Value	Count	Frequency (%)
10	14	2.0%
8	8	1.1%
7	9	1.3%
6	3	0.4%
5	6	0.9%

class
Categorical

Distinct	2
Distinct (%)	0.3%
Missing	0
Missing (%)	0.0%
Memory size	5.5 KiB

2	458
4	241

Frequencies
Length

Value	Count	Frequency (%)
2	458	65.5%
4	241	34.5%

Frequencies of value counts

Unique

Unique	0 ?
Unique (%)	0.0%

Histogram of lengths of the category

Length

Max length	1
Median length	1
Mean length	1
Min length	1

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

First rows

	sample	thickness	size_unif	shape_unif	marginal_adhesion	epithelial_cell_size	bare_nuclei	bland_chromatin	normal_nucleoli	mitoses	class
0	1000025	5	1	1	1	2	1.0	3	1	1	2
1	1002945	5	4	4	5	7	10.0	3	2	1	2
2	1015425	3	1	1	1	2	2.0	3	1	1	2
3	1016277	6	8	8	1	3	4.0	3	7	1	2
4	1017023	4	1	1	3	2	1.0	3	1	1	2
5	1017122	8	10	10	8	7	10.0	9	7	1	4
6	1018099	1	1	1	1	2	10.0	3	1	1	2
7	1018561	2	1	2	1	2	1.0	3	1	1	2
8	1033078	2	1	1	1	2	1.0	1	1	5	2
9	1033078	4	2	1	1	2	1.0	2	1	1	2

Last rows

	sample	thickness	size_unif	shape_unif	marginal_adhesion	epithelial_cell_size	bare_nuclei	bland_chromatin	normal_nucleoli	mitoses	class
689	654546	1	1	1	1	2	1.0	1	1	8	2
690	654546	1	1	1	3	2	1.0	1	1	1	2
691	695091	5	10	10	5	4	5.0	4	4	1	4
692	714039	3	1	1	1	2	1.0	1	1	1	2
693	763235	3	1	1	1	2	1.0	2	1	2	2
694	776715	3	1	1	1	3	2.0	1	1	1	2
695	841769	2	1	1	1	2	1.0	1	1	1	2
696	888820	5	10	10	3	7	3.0	8	10	2	4
697	897471	4	8	6	4	3	4.0	10	6	1	4
698	897471	4	8	8	5	4	5.0	10	4	1	4

Most frequent

	sample	thickness	size_unif	shape_unif	marginal_adhesion	epithelial_cell_size	bare_nuclei	bland_chromatin	normal_nucleoli	mitoses	class	count
0	320675	3	3	5	2	3	10.0	7	1	1	4	2
1	466906	1	1	1	1	2	1.0	1	1	1	2	2
2	704097	1	1	1	1	1	1.0	2	1	1	2	2
3	1100524	6	10	10	2	8	10.0	7	3	3	4	2
4	1116116	9	10	10	1	10	8.0	3	3	1	4	2
5	1198641	3	1	1	1	2	1.0	3	1	1	2	2
6	1218860	1	1	1	1	1	1.0	3	1	1	2	2
7	1321942	5	1	1	1	2	1.0	3	1	1	2	2

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows

Duplicate rows

Most frequent